Curves are a transition from one line to another such that a curved line
emerges.
For doing so one needs to interpolate between 4 points.

curve is a simple curve with linear interpolation twice;
looks quite curvy anyway

smooth is a smoother interpolation with continous derivations at its end
when continuing with the constant 0 or 1 function

f(0) = 0
f(1) = 1
f'(0) = 0
f'(1) = 0

f = bx^3+cx^2+dx+e
f' = 3bx^2 + 2cx + d

f(0) = 0 -> e=0
f(1) = 1 -> b+c+d+e = 1
f'(0) = 0 -> d = 0
f'(1) = 0 -> 3b+2c+d = 0

b+c = 1
3b+2c = 0

c = 3
b = -2

-2*$x*$x*$x+3*$x*$x

circ is an interpolation that results in a proper quarter circle when
used on two interpolation base lines of the same length that have a
common vertex

      \
       \
--------U----+
-----....\   |
         "X  |
          \\ |
           \\|
            |V
            ||\
            || \

X = (cos phi, sin phi) = (x,y)

l = (x + µ y, y - µ y)

U = (x + µ1 y, y - µ1 x = 1)
V = (x + µ2 y = 1, y - µ2 x)

µ1 = (y-1)/x
µ2 = (1-x)/y

U = (x + y(y-1)/x, 1)
V = (1, y - x(1-x)/y)

dxU = y(y-1)/x
dyU = 1-y
dxV = 1-x
dyV = x(1-x)/y

l1 = sqrt (dxU*dxU + dyU*dyU)
l2 = sqrt (dxV*dxV + dyV*dyV)